The pig family is going on a picnic during the holiday. However, Mr Bull and the constructors are constructing the road while they were traveling to the park. There are a total of $N$ workers, the 1-st worker is at the front of the road and the $N$-th worker is at the back. Given that the $i$-th worker will let go a car after every $C_i$ seconds. There are a total of $K$ cars, output the location of every car from the 1-st to the $T$-th second.

Simulation:

Input

The first line contains three integers, $N, K, T$.
The second line contains $N$ integers, where the $i$-th integer is $C_i$.

Output

Output the location of every car from the 1-st to the $T$-th second, in $T$ lines, following the format of the sample case.

Constraints

For all test cases: $1 \le N,K \le 100$, $1 \le T \le 10^4$, $1 \le C_i \le 10^3$
Subtask 1 (30%): $N = 1$
Subtask 2 (30%): $K = 1$
Subtask 3 (40%): No additional constraints